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2 years ago

What will happen to the period of a ball-on-a-spring if the ball is replaced by a smaller one with half the mass

Physics

1 answer:

Murrr4er [49]2 years ago

4 0

When the ball on a spring is replaced by a smaller ball with half the mass : The period decrease by 29%

<h3>Calculate the Period </h3>

We will apply the formula below to calculate period

T = $2\pi \sqrt{\frac{m}{k } }$

where :

T₁ / T₂ = $\sqrt{\frac{m_{1} }{m_{2} } }$ where m₂ = m₁ / 2

Therefore :

T₂ = $\frac{T_{1} }{\sqrt{2} }$ = 0.71 T

Hence we can conclude that the period will decrease by 29% ( i.e 100 - 71 ).

Learn more about Period calculation : brainly.com/question/10728818

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A slender rod is 90.0 cm long and has mass 0.120 kg. A small 0.0200 kg sphere is welded to one end of the rod, and a small 0.070

likoan [24]

Given Information:

length of slender rod = L = 90 cm = 0.90 m

mass of slender rod = m = 0.120 kg

mass of sphere welded to one end = m₁ = 0.0200 kg

mass of sphere welded to another end = m₂ = 0.0700 kg (typing error in the question it must be 0.0500 kg as given at the end of the question)

Required Information:

Linear speed of the 0.0500 kg sphere = v = ?

Answer:

Linear speed of the 0.0500 kg sphere = 1.55 m/s

Explanation:

The velocity of the sphere can by calculated using

ΔKE = ½Iω²

Where I is the moment of inertia of the whole setup ω is the speed and ΔKE is the change in kinetic energy

The moment of inertia of a rigid rod about center is given by

I = (1/12)mL²

The moment of inertia due to m₁ and m₂ is

I = (m₁+m₂)(L/2)²

L/2 means that the spheres are welded at both ends of slender rod whose length is L.

The overall moment of inertia becomes

I = (1/12)mL² + (m₁+m₂)(L/2)²

I = (1/12)0.120*(0.90)² + (0.0200+0.0500)(0.90/2)²

I = 0.0081 + 0.01417

I = 0.02227 kg.m²

The change in the potential energy is given by

ΔPE = m₁gh₁ + m₂gh₂

Where h₁ and h₂ are half of the length of slender rod

L/2 = 0.90/2 = 0.45 m

ΔPE = 0.0200*9.8*0.45 + 0.0500*9.8*-0.45

The negative sign is due to the fact that that m₂ is heavy and it would fall and the other sphere m₁ is lighter and it would will rise.

ΔPE = -0.1323 J

This potential energy is then converted into kinetic energy therefore,

ΔKE = ½Iω²

0.1323 = ½(0.02227)ω²

ω² = (2*0.1323)/0.02227

ω = √(2*0.1323)/0.02227

ω = 3.45 rad/s

The linear speed is

v = (L/2)ω

v = (0.90/2)*3.45

v = 1.55 m/s

Therefore, the linear speed of the 0.0500 kg sphere as its passes through its lowest point is 1.55 m/s.

8 0

3 years ago

I really need help with this problem ;)

Nesterboy [21]

They're never the same ray.

4 0

3 years ago

Read 2 more answers

if a free falling rock were equipped with a speedometer, by how much would it's speed readings increase with each second IF it w

Kaylis [27]

Accelleration(a) is changing of velocity in second.
free fall a = g
speed increase = a = g = 20 (m/s) / s

7 0

3 years ago

Which actions are evidence that a chemical reaction has occurred? Check all that apply. a change in color the formation of a pre

NeTakaya

Answer:

a change in color
the formation of a precipitate
the formation of bubbles

Explanation:

In a chemical reaction, there is always a rearrangement of atoms within the molecules of reactants to form new products. Such a change is different from changes in the physical form of molecules, e.g. shape.

Thus, according to this criteria, only three options are correct in the given question. A change in color is definitely an indication of chemical reaction because the emission of light before and after cannot be changed unless molecules are rearranged to form a new chemical. Likewise, precipitates form when a reaction takes place between chemically dissolved molecules to form less or not dissolvable compounds. In the end, the configuration of bubbles also indicates that the reaction has taken place because new gases are being released.

On the other hand, change in shape is a physical change because the composition doesn't need to also been changed. An example is the ice formation from water. Same is the case with "change of clear liquid to cloudy" because the addition of non-reactive substances could change the nature of liquid to cloudy however the reaction doesn't need to have taken place.

8 0

3 years ago

Read 2 more answers

Derive the following equations of motion

xz_007 [3.2K]

Answer:

___________________________________

<h3>a. Let us assume a body has initial velocity 'u' and it is subjected to a uniform acceleration 'a' so that the final velocity 'v' after a time interval 't'. Now, By the definition of acceleration, we have:</h3>

$a = \frac{v - u}{t} \\ or \: at = v - u \\ v = u + at \:$

It is first equation of motion.

___________________________________

<h3>b. Let us assume a body moving with an initial velocity 'u'. Let it's final body 'v' after a time interval 't' and the distance travelled by the body becomes 's' then we already have,</h3>

$v = u + at...........(i) \\ s = \frac{u + v}{2} \times t.........(ii)$

Putting the value of v from the equation (i) in equation (ii), we have,

$s= \frac{u + (u + at)}{2} \times t \: \: \\ or \: s = \frac{(2u + at)t}{2} \\ or \: s = \frac{2ut + a {t}^{2} }{2} \\ s = ut + \frac{1}{2} a {t}^{2}$

It is third equation of motion.

________________________________

<h3>c. Let us assume a body moving with an initial velocity 'u'. Let it's final velocity be 'v' after a time and the distance travelled by the body be 's'. We already have,</h3>

$v = u + at.....(i) \\ s = \frac{u + v}{2} \times t......(ii) \\$

$v = u + at \\ or \: at = v - u \\ t = \frac{v - u}{a}$

Putting the value of t from (i) in the equation (ii)

$s = \frac{u + v}{2} \times \frac{v - u}{a} \\ or \: s = \frac{ {v}^{2} - {u}^{2} }{2a} \\ or \: 2as = {v}^{2} - {u}^{2} \\ {v}^{2} = {u}^{2} + 2as$

It is forth equation of motion.

________________________________

Hope this helps...

Good luck on your assignment..

3 0

3 years ago